The Non-Strict Projection Lemma

Fuente: arXiv
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Autori principali: Meijer, T. J., Holicki, T., Eijnden, S. J. A. M. van den, Scherer, C. W., Heemels, W. P. M. H.
Natura: Preprint
Pubblicazione: 2023
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author Meijer, T. J.
Holicki, T.
Eijnden, S. J. A. M. van den
Scherer, C. W.
Heemels, W. P. M. H.
author_facet Meijer, T. J.
Holicki, T.
Eijnden, S. J. A. M. van den
Scherer, C. W.
Heemels, W. P. M. H.
contents The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear-matrix-inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation.
format Preprint
id arxiv_https___arxiv_org_abs_2305_08735
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The Non-Strict Projection Lemma
Meijer, T. J.
Holicki, T.
Eijnden, S. J. A. M. van den
Scherer, C. W.
Heemels, W. P. M. H.
Optimization and Control
Systems and Control
The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear-matrix-inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation.
title The Non-Strict Projection Lemma
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2305.08735